The present invention relates to a vibration test system for structures and a vibration test method implemented therein. In particular, the present invention is concerned with a vibration test system and method for structures that perform in combination a vibration test on part of a structure and numerical analysis of a vibrational response.
A vibration test in which a vibration test on part of a structure and numerical analysis of a vibrational response are performed in combination is called a “actuator-computer online test.” An example of an actuator-computer online test system is described in, for example, the report collection published from Architectural Institute of Japan (Vol. 288, 1980, pp. 115–124). As described in the literature, a central difference method that is one of explicit time integral approaches obviating the necessity of convergence is adopted as time integration required for numerical analysis of a vibrational response.
Moreover, in order to sophisticate the time integration required for numerical analysis of a vibrational response employed in an actuator-computer online test, a technology of adopting an αOS method that is one of mixed integral approaches of the explicit and implicit time integral approach is introduced in, for example, “Numerical Integration Method for Experimentation of Tentatively Moving a Substructure providing an Experimentation Error Control Effect” (report collection published from Architectural Institute of Japan, Vol. 454, pp. 61–71, 1993). The αOS method is a time integration method that is a mixture of an OS method which remains stable even when the calculation time interval is set to a large value, and an α method that is an implicit time integral approach for damping a high-order mode of vibration serving as a factor of an error. The αOS method is a time integration method suitable for the actuator-computer online test. According to the αOS method, a restoring force exerted by a structure to be assessed is divided into a linear component and a nonlinear component. The explicit time integral approach is applied to the nonlinear component of the restoring force exerted by the structure, and the implicit time integral approach is applied to the other component of the restoring force.
The central difference method is one of explicit time integral approaches for predicting a deformed state attained at a current time step from the deformed state observed at the previous time step. In the actuator-computer online test, a target displacement is obtained by calculating a vibrational response. An actuator is driven to cause the target displacement. When a reaction of a specimen is detected, the test proceeds to the next step. This procedure is repeated. The central difference method needs to determine a calculation time interval on the basis of the shortest natural period of a structure, of which reaction is to be calculated, because of restrictions imposed for stable condition.
Therefore, when a structure to be assessed is complex, it is necessary to not only increase the freedom in a vibrational equation but also reduce a calculation time interval along with a decrease in the natural period of the structure. This poses a problem in that a load on calculation increases. Moreover, when the calculation time interval is reduced, a change in a vibratory displacement caused by an actuator at a time step is diminished. This poses a problem in that precision in excited vibration deteriorates and an error in a high-order mode of vibration takes place.
Moreover, a method widely used for numerical analysis of a vibrational response is what is called an implicit time integral approach. According to the implicit time integral approach, a calculation time interval can be increased irrespective of the natural period of a structure to be assessed. However, the implicit time integral approach requires convergence of a deformed state attained at a current time step on the basis of a balance of forces at the current time step. When the structure to be assessed exhibits a nonlinear characteristic, the convergence becomes complex. Consequently, since an actuator must be driven according to the complex convergence process, the implicit time integral approach is unsuitable for the actuator-computer online test.
In order to improve the precision in the actuator-computer online test, there is a demand for a time integral approach capable of controlling an experimental error, which causes an error in a high-order mode of vibration, and of remaining stable despite a long interval between calculations.
In recent years, improvement in the aseismatic performance of an architectural structure or a plant structure or improvement in precision in assessing aseismatic strength has been demanded. Moreover, exploitation of an actuator-computer online test has been expected. The capability to assess more complex structures as well as the improvement in the precision in the assessment has been demanded. This causes a numerical model portion of a structure to become larger in size and more complex, and necessitates introduction of a nonlinear finite element method. Formulation based on an incremental equilibrium equation having as an unknown an incremental displacement between time steps has become the mainstream of time integration employed in numerical analysis of a vibrational response required by the nonlinear finite element method, because the formulation is superb in convergence.
In contrast, the αOS method adapted to an actuator-computer online test described in the aforesaid non-patent document “Numerical Integration Method for Experiment of Tentatively Moving a Substructure providing an Experimental Error Control Effect” is based on an equilibrium equation having as an unknown a displacement itself occurring at each time step. Therefore, the αOS method can handle only a linear model as a model representing a numerical model portion in practice.